Mathematical Basis for Physical Inference

While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.Comment: 24 pages, 4 figure

Machine-Checked Proofs For Realizability Checking Algorithms

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions, assume/guarantee contracts, and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. For these proofs to be meaningful, each leaf-level component contract must be realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. We have recently proposed (in [1]) a contract-based realizability checking algorithm for assume/guarantee contracts over infinite theories supported by SMT solvers such as linear integer/real arithmetic and uninterpreted functions. In that work, we used an SMT solver and an algorithm similar to k-induction to establish the realizability of a contract, and justified our approach via a hand proof. Given the central importance of realizability to our virtual integration approach, we wanted additional confidence that our approach was sound. This paper describes a complete formalization of the approach in the Coq proof and specification language. During formalization, we found several small mistakes and missing assumptions in our reasoning. Although these did not compromise the correctness of the algorithm used in the checking tools, they point to the value of machine-checked formalization. In addition, we believe this is the first machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur

Computing Persistent Homology within Coq/SSReflect

Persistent homology is one of the most active branches of Computational Algebraic Topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this paper, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories

The effect of contextual variables in the relationship between CSR and CFP: Evidence from Indonesian companies

The objectives of this study is to investigate whether business environment, business strategy, formalization, decentralization, reliance on combination of belief & boundary system, reliance on combination of diagnostic & interactive control system, reliance on interactive control system moderate the relationship between CSR and CFP under the slack resource and good management theories. 220 respondents from manufacturing companies listed on the Jakarta Stock Exchange were selected and two regression models were developed to examine the relationship between the related variables. The findings show that business environment has moderated the CSR-CFP link under good management theory, decentralization has moderated the CSR-CFP link under slack resource theory, and reliance on combination of diagnostic and interactive control system has moderated the CSR and CFP link based on slack resource theory

SMT-Friendly Formalization of the Solidity Memory Model

Solidity is the dominant programming language for Ethereum smart contracts. This paper presents a high-level formalization of the Solidity language with a focus on the memory model. The presented formalization covers all features of the language related to managing state and memory. In addition, the formalization we provide is effective: all but few features can be encoded in the quantifier-free fragment of standard SMT theories. This enables precise and efficient reasoning about the state of smart contracts written in Solidity. The formalization is implemented in the solc-verify verifier and we provide an extensive set of tests that covers the breadth of the required semantics. We also provide an evaluation on the test set that validates the semantics and shows the novelty of the approach compared to other Solidity-level contract analysis tools.Comment: Authors' manuscript. Published in P. M\"uller (Ed.): ESOP 2020, LNCS 12075, 2020. The final publication is available at Springer via https://doi.org/10.1007/978-3-030-44914-8_

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page